A fair coin is tossed three times. Let [math]X[/math] be the number of heads that turn up on the first two tosses and [math]Y[/math] the number of heads that turn up on the third toss.

Give the distribution of

• the random variables [math]X[/math] and [math]Y[/math].
• the random variable [math]Z = X + Y[/math].
• the random variable [math]W = X - Y[/math].